State Operation Optimization in Electrical NetworksPaulo Pereira‡, Sergio Leitao‡, E. J. Solteiro Pires†‡

† INESC TEC – INESC Technology and Science (formerly INESC Porto, UTAD pole)‡Escola de Ciencias e Tecnologia, Universidade de Tras-os-Montes e Alto Douro, 5000–811 Vila Real, Portugal

Email: paulo haggs@hotmail.com, {sleitao,epires}@utad.pt

Abstract—This paper makes a study about optimal supplyof the energy service, using simulations of network operationscenarios, in order to optimize resources and minimize thevariables: operation cost, energy losses, generation cost andconsumers shedding. These simulations create optimal operationmodels of the network, allowing the system operator obtainknowledge to take pre-established procedures that must beperformed in situations of contingency in order to forecast andminimize drawbacks. The simulations were performed usinga multiobjective particle swarm optimization algorithm. Thealgorithm was applied to the IEEE 14 Bus network wherethe optimal power flow was evaluated by MATPOWER tool toestablish an optimal electrical working model to minimize theassociated costs.

Keywords-Optimal Power Flow, Multiobjective Particle SwarmOptimization Algorithm, Multiobjective Problem.

I. INTRODUCTIONEnergy is probably the main driver of possible agent for

future development models at a global scale. Satisfy realtime demanding in each point of the network implies a newmanagement approaches to ensure a high quality of the energysupply. With the increasing of energy systens complexity, theoperation of the networks in optimal control limits, will be atcapacity and profitability of supply, requires optimization ofmultiple objectives.The increasing introduction of distributed generation in

power systems ceases the existence of a well controlled andcentralized production in a few producers to have a decen-tralized production, that is associated to some unpredictabilityand uncertainty which imposes new challenges to the energyoperators. Additionally, there is an increased consumption ofelectrical energy, expansion of electric power grids, growingconcerns about environmental and sustainability, the increasingassociated development of distributed energy technologies and,finally, the growing requirement by consumers in terms ofpower quality. Several of these problems have been suc-cessfully solved using particle swarm optimization algorithm(PSO). For instance, the PSO algorithms have been used,obtaining promising solutions, in many electrical energy ap-plications, including, in voltage control of distribution net-works with microgrids [1], in solving problems of optimalconfiguration in the distribution system to minimize powerloss [2], in dynamic optimal reactive power dispatch [3],in optimization of biomass fuelled systems for distributedpower generation [4], in power flow technique consideringtwo objectives: generation cost and environment pollution [5],among many others.

This paper characterizes and defines the profile of thenetwork model test, performs some simulations to determinethe optimal operation point. A multiobjective particle swarmoptimization algorithm (MOPSO) was used to find the optimaloperation point. The paper is organized as follows. Section IIdescribes the MOPSO algorithm and their basic principles.Next, in section III, is made a brief introduction of importanttopics related to power flow, its importance and usefulness inthe planning and operation of the electric power systems. Sec-tion IV formulates the problem and methodology for collectingand analyzing data of case study. In section V, is characterizedand defined the profile of the network test model and thenMOPSO algorithm is implemented to optimize the operatingstate and determine the optimal function of the system. Itpresented the different tests performed and results obtained.Finally, section VI draws the main conclusions resulting fromthe research, the scenarios and the developed discussion.

II. MULTIOBJECTIVE PARTICLE SWARM OPTIMIZATION

PSO algorithm is based on a series of biological mecha-nisms, particularly in the social behavior of animal groups[6]. It consists of particles movement guided by the mostpromissing particle and the best location visited by eachparticle. The fact they work with stochastic operators andseveral solutions, provides PSO the ability to escape from localoptimum and maintain a diverse population. Moreover, theability to work with a population of solutions simultaneouslyintroduces a global horizon and a wider search variety, makingpossible a more comprehensive assessment of the search spacein each iteration. These characteristics ensure a higher abilityto find the global optimum in problems that have multiplelocal optimum.Most part of real problems have more than one objective

to be optimized. Therefore, several techniques were proposedto solve multiobjective problems. Additionally, many of theapproaches and principles that had already been explored indifferent types of evolutionary algorithms have been adoptedor adapted into the MOPSO [7].For solving a multiobjective optimization problem seeks to

find an acceptable set of solutions instead of uniobjectivo prob-lems, where there is only one solution (except in cases whereuniobjective functions have more than one global optimum).Solutions in multiobjective optimization problems intend acompromise between different criterias, enabling the existenceof several optimal solutions. It is common to use the concept of

1st BRICS Countries Congress on Computational Intelligence

978-1-4799-3194-1/13 $31.00 © 2013 IEEE

DOI 10.1109/BRICS-CCI.&.CBIC.2013.60

350

1st BRICS Countries Congress on Computational Intelligence

978-1-4799-3194-1/13 $31.00 © 2013 IEEE

DOI 10.1109/BRICS-CCI.&.CBIC.2013.60

350

2013 BRICS Congress on Computational Intelligence & 11th Brazilian Congress on Computational Intelligence

978-1-4799-3194-1/13 $31.00 © 2013 IEEE

DOI 10.1109/BRICS-CCI-CBIC.2013.65

350

1: t = 02: Random initialization of P (t)3: Evaluate P (t)4: A(t) =Selection of non-dominated solutions5: while the process do6: for Each particle do7: Select pg

8: Change position9: Evaluate particle10: Update p11: end for12: A(t)= Selection(P (t) ∪ A(t))13: t = t + 114: end while15: Get results from A

Fig. 1. The Structure of MOPSO Algorithm

dominance to compare the various solutions of the population.The final solutions are represented graphically by a front.Figure 1 illustrates a simple MOPSO algorithm. After the

swarm initialization, several loops are performed in order toincrease the quality of the population and archive. In a loopt, each population particle selects a particle guide from thearchive A(t). Based on the guide and personal best, eachparticle moves according simple PSO formulas. At the end ofthe loops, the archive is updated selecting the non-dominantsolutions among population, P (t), and archive. When the non-dominant solution number is greater than the size of archive,the solutions with best diversity and extension are selected.The process comes to an end, usually after a certain numberof iterations.

III. ELECTRICAL POWER SYSTEMSOne of the most widely used forms of energy today is

electricity, thanks to its portability and low rate of energy lossduring conversion. Electrical energy, at global level, is ob-tained mainly from thermoelectric power plants, hydropowerplants, wind farms and nuclear power plants. Electrical poweris seen as the “engine” of modern society.Conventionally, the power plants have been large centralized

units of electricity, but the new trend is for the development ofDistributed Generation (DG) units of energy. The concept of adistributed power system refers to an energy system in whichthe energy conversion units are located close to consumers.Besides the distribution of technology, there is a whole systemof distributed energy, re-allocation of decision-making skillsand responsibility in terms of energy supply. In practice, theenergy system in the future will be a combination of cen-tralized and distributed centralized subsystems, operationallyparallel to each other [8].The DG, generally defined as the generation of electricity

on a small scale, is just a new concept in the vocabulary of theelectricity market economy, but the idea behind this conceptis not new at all. In the early generation of electricity, DG wasthe rule and not the exception [9]. The power generated willbe relatively low, typically on the order of 15 kW to 10 MWto feed local loads.The concept of acceptable penetration level refers to the

maximum power capacity of DG connected to distributionnetwork capable of ensuring that the system can operate

safely, securely and economically reliable. The penetrationlevel refers to many factors, such as the short-circuit current,stability, reliability [10]. Therefore, it will be a very compli-cated problem to calculate the penetration level, if all factorsare considered and the result might also not be consensual.According to [9], the electricity generation by small particu-

lar units could result in 30% of the electricity reduction cost intransmission and distribution. As such, the DG is seen as oneof the most important factors in combating the demand in thesector. Generally, the smaller the volume of the customer, thegreater the proportion of transmission and distribution costs inthe electricity price (over 40%).Therefore, entities responsible for transmission and distribu-

tion need to be equipped with analytic tools and applicationsto evaluate the impact of various DG sources, connected tothe network, from the point of view of supply reliability,operating stability and tension quality. One way of analyzingand evaluating the impact of DG penetration in distributionnetworks are the power flow studies.

A. Power Flow in Distribution NetworkThe operation mode of electrical power systems usually

depends on the variation of conditions slowly over time,allowing a similar analysis to a system in steady state. Thepower flow, also called Load Flow and, more recently, byPower Flow is thus a steady state solution of electrical powersystems, which includes the generators, the network and loads.It is based on determining the voltage profile across all nodesof the network and of the active and reactive power flow inlines and transformers, for conditions of generation and loadspecified for a given configuration and topology.The power flow problem is fairly difficult in their full

format, coinciding the fact that it is mathematically non-linear and the imposition of restrictive conditions for variousvalues of quantities. It is a more common tool used in theelectrical networks analysis. Studies involving the power flowcalculation are important, both in planning and in exploitationof electrical power systems. In order to make decisions aboutthe future structure of electrical power systems and its con-stitution, among other things, it is necessary to consider theconsumption increases, which makes it inevitable to simulatethe system behavior under different circumstances.Due to the large number of nodes (buses) and branches

(lines and transformers) a system of large-scale means thatthe model equations are nonlinear, which requires robustand efficient calculating methods. The process of solving aproblem of power flows problem encompasses:• The formulation of a mathematical model that representswith sufficient rigor the actual physical system;

• The specification of the type of buses and quantities foreach one;

• Determine the numerical solution of the power flowequations, which provides the value of the amplitudesand arguments voltages in all buses;

• Evaluate the powers that flows in all branches (lines andtransformers).

351351351

The multiple system components are only the nodes (buses)and branches (lines, transformers and capacitor banks) sincethe cutting and protection equipment and other system ele-ments have no influence in the result. Moreover, it is assumedthat the three phase system is symmetrical and balanced, sothe analysis is unifilar, i.e., only one phase study.The total load distribution of the system by production

centers is called dispatch. Since the losses are not knownin advance, the order is made against an estimate of losses(e.g., 5 to 8% of the total load) and in this case the buscompensation is mandated to do final settlement of the balanceequation [11]. Usually, it takes a bus to the origin of this phase,i.e., as reference phase bus (θ = 0

◦

). Besides this bus, chosenfrom among the generation, there are generation buses (whereare power plants) and also use the buses consumer (wheredoes not exist generation) or fixed generation, where it meetsSG = PG + jQG.

B. Optimal Power FlowAll the usual functionality of case studies of typical models

used in power flow problems are analyzed by means ofmodeling AC and DC.The DC modeling is based on linearization of the power

flow expressions, i.e., a simplified strategy resolution. Theequations linearization allows the direct resolution of theproblem, through certain simplifications generally accepted inthe networks of higher voltages, with the airlines. In this paperwas used the AC modeling, where the loads, both the activeand the reactive injections are modeled as constant power, Pd

and Qd. The shunt admittance, Ysh, is evaluated by Gsh andBsh using the equation (1) where Gsh is the condutance shunt,Bsh is the suceptance shunt, base is the base of apparent powerin MVA.

Ysh =Gsh + jBsh

base [MVA](1)

The Π model is used to model transmission lines andtransformers, using for that propose the resistance R, thereactance X , the capacitance of line load Bc, and a phasetransformer with a transformation ratio τ and a voltage angleθshift. The current value circling in bus i to bus k is given bythe relation (2): [

Ii

Ik

]= Yik

[Vi

Vk

](2)

where the admittance matrix values, Yik , are given by (3):

Yik =

[(Ys + jBc

2 ) 1τ2 −Ys

1τejθshift

−Ys1

τe−jθshiftYs + jBc

2

](3)

where, Ys , is evaluated by (4).

Ys = 1R+jX (4)

The admittances array elements of each branch and theshunt admittances for each bus are combined forming an

complex admittances array (Ybus) that relates the current(Ibus) and voltage (Vbus), both in complex form (5).

Ibus = Ybus.Vbus (5)

In the same way, it is obtained the total values of linecurrents (6):

{Ii = Yi.Vbus

Ij = Yj .Vbus

(6)

using the complex matrices, the value of the apparent power(S) injected into the buses and branches (from i to k) isexpressed by equation (7).

⎧⎪⎨⎪⎩

Sbus = diag(Vbus).I∗busSi = diag(Vi).I

∗

i

Sk = diag(Vk).I∗k

(7)

Where, Vi and Vk represent the voltage vectors of the respec-tive bus that make up the branch and diag corresponds todiagonal elements of a matrix.The conduct of the operation regime of an electric power

must be made to optimize the generation cost and ensuresafety and quality in the supply of electrical power [12].The Optimal Power Flow problem (OPF) aims to determinethe optimal operation of an electric power system based onthe objective function, which should be minimize the powerlosses, the operating costs, the actions number to be taken intocontingency situations or load shedding, and their associatedconstraints, which makes the problem very complex.The most common approach for solving the power flow

equations is using the Newton-Raphson method. This methodis an iterative approach to solve continuous nonlinear equa-tions. The Newton-Raphson method is the reference in solvingpower flow, converging frequently, in three to five iterations,regardless of the buses number in the network, provided thatno infringement of reactive power limits that require changingthe node type. Therefore is also the method used in this workto solve the power flow problem.The iterative process of calculating the bus voltages have

the following steps:1) Estimation the initial values of bus voltages.2) Calculate the errors ΔPi and ΔQi (8) between the spec-ified values and calculated active and reactive powersinjected. The equations that express the equilibrium ofactive and reactive power on the bus i is given by (9).{

ΔP ki = P

specifiedi − P calck

i

ΔQki = Q

specifiedi −Qcalck

i

(8)

P calci =

n∑k=1

Vi.Vk{Gik cos(θi− θk)+Bik sin(θi− θk)}

(9a)

352352352

Qcalci =

n∑k=1

Vi.Vk{Gik sin(θi− θk)−Bik cos(θi− θk)}

(9b)3) Calculate the Jacobian matrix, Jk:

Jk =

[H N

M L

](10)

where J is an asymmetric matrix, that possesses a topol-ogy symmetric to a not diagonal element (not null) in theupper triangle corresponds to an element (not null) in thelower triangle. Its elements are calculated analyticallyfrom the power flow equations, obtaining: (11) for i �= k,

Hik = Lik = Vi.Vk{Gik sin(θi−θk)−Bik cos(θi−θk)}(11a)

Nik = −Mik = Vi.Vk{Gik cos(θi−θk)+Bik sin(θi−θk)}(11b)

and (12) for i = k,⎧⎪⎪⎪⎨⎪⎪⎪⎩

Hii = −Qi −Bii.V2i

Nii = Pi + Gii.V2i

Mii = Pi −Gii.V2i

Lii = Qi −Bii.V2i

(12)

4) Calculate the incrementsΔθ andΔV from the followingsystem equations (13):»

ΔPk

ΔQk

–= J

k

"Δθk

ΔV k

V k

#(13)

5) Update the values of the voltage amplitude and voltagephase, for buses PQ (14):{

V k+1i = V k

i + ΔV ki

θk+1i = θk

i + Δθki

(14)

6) Update the value of voltage phase, to buses PV throughthe equation (15):

θk+1i = θk

i + Δθki (15)

and calculate the reactive power injected using theequation (16), where i = 1, 2, . . . , n.

Qcalci =

n∑k=1

Vi.Vk{Gik sin(θi − θk)−Bik cos(θi − θk)}

(16)7) If the reactive power is outside the range imposed by thegenerator, the bus will be reclassified as false PQ. In thenext iteration is calculated the reactive power, using thespecified voltage for all PV buses if the reactive poweris within the limits of the bus be classified as PV.

8) The process is repeated until the convergence isachieved, which is reached when the absolute valuesof the errors closing ΔPi and ΔQi are less thana tolerance ε arbitrarily small (e.g. 0.01 MW/Mvar):|ΔPi|, |ΔQi| < ε

IV. DEVELOPMENTHowever, at a time when the focus and the incentive, world-

wide, are the means to rationalize and minimize operationalcosts in various sectors of human activity in order to increasetheir efficiency, it was considered to be of interest to analyzepossible scenarios for operations attempting to minimize theassociated costs.To establish the sets of simulation tests that will be

done using the MOPSO algorithm in conjunction with MAT-POWER [12], to evaluate the Optimal Power Flow (OPF), isestablished an optimal operating model for the IEEE bus 14electrical network. The problem considers relevant objectivefunctions: minimize operating and investment costs. Therewas data on the local electricity network for the realizationof simulations test that allow to create an optimal operatingmodel with different scenarios.The model electricity network used in the study was the

IEEE bus network [13]. The network have 4 PV buses, 9 PQbuses, 1 compensation and reference bus (CR), 20 branchesand 5 generators (with 772.4 MW of total active power and148.0 Mvar of total reactive power).The test system used represents a part of the network of

American Electric Power Company, despite the data presentedare the setting in February 1962, this system is considered ref-erence for studies and concept testing in technical publications,particularly in studies related to power systems.

A. Functions OptimizationIn the paper two objetives are considered. The first one is

the generation cost, f1, given by expression (17) subject to theconstraints (18). Where, the parameters f i

P and f iQ represent

the cost associated with the generation of active and reactivepower, respectively, for the generator i. The functionmin f(x)is the objective function where, the nb represent vectors ofvoltage angles θ and magnitudes V and the ng vectors ofgenerator active and reactive power injections Pg and Qg.

f1 = minθ,V,Pg,Qg

ng∑i=1

{f iP (pi

g) + f iQ(qi

g)} (17)

θrefi ≤ θi ≤ θrefi , i = irefvi,min

m ≤ vim ≤ V i,max

m , i = 1, 2, ..., nb

pi,ming ≤ pi

g ≤ pi,maxg , i = 1, 2, ..., ng

qi,ming ≤ qi

g ≤ qi,maxg , i = 1, 2, ..., ng

(18)

The second function, f2, is the investment cost (19), wheren is the number of generation buses. The function f2 consistsof a constant part β1, that represents the power plant cost,and a variable part β2, that depends of the power plantcapacity. The function optimization consists of f1 and f2,where the objective is to minimize both the generation costand investment cost simultaneously.

f2 =

n∑i=1

{β1 + β2(Pi + jQi)2} (19)

353353353

V. TESTS AND RESULTSIn the OPF problem the active and reactive power generated

was limited. The restriction to consider upper and lower limitsof the power produced at each bus is due to MATPOWER cannot specify or assign the values of active (PG) and reactive(QG) power that have to be generated by each bus. TheIEEE 14 bus network consists has 5 generators, where G1

correspond to the reference bus, that only generates energy,i.e. has no consumption. The minimum value of PG

i [MW]and QG

i [Mvar] considered in simulations is 0 for all the busgenerators.Two possible scenarios of test network operation were

performed in which they were seen the profiles shown in figure2. The profile of relevant variables used are: active and reactivepower produced and consumed on the buses, bus voltage andpower losses in the branches.The MOPSO algorithm considered has 40 particles with an

archive of 20 solutions and is run during 20 iterations. Duringthe execution of MOPSO algorithm, the parameter w decreaseslinearly from 0.7 to 0.4 and acceleration coefficients φ1 and φ2

follows an random uniform distribution in the interval [0, 1.4].The constants used in function f2 are β1 = 100 and β2 =10−4.

A. Scenario IFor Scenario I, the MOPSO algorithm parameters remain

the same for the three test cases of simulations (see Table I).The parameters of the OPF problem, ranges with respect tothe generators out of service (Gi = 0) over the cases of thisscenario, i = {1, 2, 3} (see Table I).

TABLE IPARAMETERS OF THE OPF PROBLEM IN THE SCENARIO I.

Generators PG

max[MW] QG

max[Mvar]

Case I G2, G3, G6, G8 350 350G1 0 0

Case II G1, G3, G6, G8 350 350G2 0 0

Case III G1, G2, G6, G8 350 350G3 0 0

Figure 3 shows the obtained front for the 3 cases. Each casehave some possible non-dominated solutions that the decisionmaker could choose according to its preferences. It could benoted that case III obtains better results for generation costminimization. However, case I obtains the lower investmentwith larger generation cost. This is due to the fact that G1 isassociated to the reference bus (compensation), with greatergenerating capacity and consequently lower cost of generationcompared to the others generators. So, if G1 is out of service,the total energy generation required is supported by the othersgenerators. Since the others generators are associated withPV buses (buses that contain generation and consumptionassociated with it) the total cost increases.Additionally, comparing the cases is noted that in case I the

maximum generation cost is higher when compared to otherscases. This fact increases the cost, as has been mentionedpreviously when the G1 is out of service over remaining

8 10 12 14 16 18 20 22 241

1.5

2

2.5

3

3.5

4

4.5

Generation Cost ($/MWh)

Inve

stm

ent C

ost (

$/M

Wh)

Case ICase IICase III

Fig. 3. Comparing performance of function optimization for the three casesof the scenario I.

generators G2 and G3, because the energy production in thesegenerators are most penalized. For the cases II and III, wherethe generators G2 and G3 are out of service, the difference isminimum, because the degree penalty costs are identical.

B. Scenario IIFor scenario II, the MOPSO algorithm parameters remain

the same as Scenario I (see Table II). However, the parametersof the OPF problem change the values of PG

max and QGmax

across the cases of this scenario, according table II.

TABLE IIPARAMETERS OF THE OPF PROBLEM IN THE SCENARIO II.

Generators PG

max[MW] QG

max[Mvar]

Case I G1, G2, G3, G6, G8 250 250Case II G1, G2, G3, G6, G8 350 350Case III G1, G2, G3, G6, G8 450 450

Figure 4 compares the three cases, where it is noted thatin case I the investment cost is a little lower comparedto the others cases. This result is obviously because theinstalled power is lower than in others cases. The minimumenergy generation cost is identical in all three cases becausethe lower cost of energy production associated with the G1

bus is penalized by additional energy losses resulting fromtransportation.

9.5 10 10.5 11 11.5 12 12.5 132

2.5

3

3.5

4

4.5

5

5.5

Generation Cost ($/MWh)

Inve

stm

ent C

ost (

$/M

Wh)

Case ICase IICase III

Fig. 4. Comparing performance of function optimization for the three casesof the scenario II.

354354354

0 5 10 15−5

0

5

10

15

20

25

Bus

Rea

ctiv

e P

ower

(Mva

r)

Reactive Power Output (Mvar)Reactive Power Demand (Mvar)

0 5 10 150

50

100

150

200

Bus

Rea

l Pow

er(M

W)

Real Power Output (MW)Real Power Demand (MW)

0 5 10 15 200

2

4

6

8

10

Branch

Loss

es −

I2 * Z

Real Losses I2 * R (MW)

Reactive Losses I2 * jX (Mvar)

0 5 10 15−15

−10

−5

0

5

Bus

Vol

tage

Voltage Magnitude (p.u.)Voltage Angle (degrees)

0 2 4 6 80

50

100

150

200

250

300

350

Generator

Max

imum

Pow

er G

ener

ated

Maximum Real Power Output (MW)Maximum Reactive Power Output (Mvar)

0 2 4 6 8−40

−35

−30

−25

−20

−15

−10

−5

0

Generator

Min

imum

Pow

er G

ener

ated

Minimum Real Power Output (MW)Minimum Reactive Power Output (Mvar)

Fig. 2. The profile of network model IEEE 14 bus for simulations test.

VI. CONCLUSION

In the present paper has been discussed some concepts aboutmultiobjective optimization. Additionally, important aspectsrelated to optimal power flow problems, in planning andexploitation of electrical power systems was addressed. Thisnetwork intended to represent a electric power system wheresome buses could be powered by distributed energy sourceswith different cost of conventional production and uncertaintyin production. A MOPSO algorithm was used to simulatedseveral scenarios in the IEEE 14 bus network. The algorithmconsiders both operational and investment costs, based onrelevant objective functions. Despite a negligible number ofexperiences and also because the objective function have onlytwo criteria, the algorithm converged to a MOPSO front, char-acterized by having an optimal set of alternatives solutions.Therefore, it could be noted that objectives are conflictingpresenting different alternative solutions along the obtainedfront. The algorithm was tested in 2 different scenarios, eachone with 3 cases. In the scenarios, simulation parameters werechanged, namely the power of some generators and varyingthe capacity of some generators. The results are promising,suggesting that the MOPSO finds non-dominated Pareto frontseasily.

ACKNOWLEDGMENT

This work has been part-funded by FCT – Fundacao paraa Ciencia e Tecnologia within project ADAPT Project –PTDC/CPE-CED/115175/2009

REFERENCES[1] A. Madureira and J. P. Lopes, “Ancillary services market framework

for voltage control in distribution networks with microgrids,” ElectricPower Systems Research, vol. 86, pp. 1–7, 2012.

[2] A. Abdelaziz, F. Mohammed, S. Mekhamer, and M. Badr, “Distributionsystems reconfiguration using a modified PSO algorithm,” ElectricPower Systems Research, vol. 79, pp. 1521–1530, 2009.

[3] Y. Li, Z. L. Yijia Cao, Y. Liu, and Q. Jiang, “Dynamic optimal reactivepower dispatch based on parallel particle swarm optimization algorithmcomputers & mathematics with applications,” Electric Power SystemsResearch, vol. 57, pp. 1835–1842, 2009.

[4] P. R. Lopez, M. G. Gonzalez, N. R. Reyes, and F. Jurado, “Optimizationof biomass fuelled systems for distributed power generation using PSO,”Electric Power Systems Research, vol. 78, pp. 1448–1455, 2008.

[5] J. Hazra and A. K. Sinha, “A multi-objective optimal power flow usingparticle swarm optimization,” European Transactions on ElectricalPower, vol. 21, no. 1, pp. 1028–1045, 2011.

[6] J. Kennedy and R. Eberhart, “Particle swarm optimization. in neuralnetworks,” IEEE International Conference, vol. 4, pp. 1942–1948, 1995.

[7] K. Deb, “Multi-objective optimization using evolutionary algorithms.”John Wiley & Sons, Chichester, UK. ISBN 0-471-87339-X, 2001.

[8] K. Alanne and A. Saari, “Distributed energy generation and sustainabledevelopment,” Helsinki University of Technology, Finland, 2006.

[9] G. Pepermans, “Distributed generation: definition, benefits and issues,”Energy Policy, vol. 33, pp. 787–798, 2005.

[10] J. Chen and R. Fan, “Penetration level optimization for dg consideringreliable action of relay protection device constrains,” National BasicResearch Program of China (973 Program) (2009CB219701), 2009.

[11] A. Pazderin and S. Yuferev, “Power flow calculation by combinationof newton-raphson method and newton’s method in optimization,” inIndustrial Electronics. 35th Annual Conf. of IEEE, 2009, pp. 1693–1696.

[12] R. D. Zimmerman and E. Murillo-Sanchez, “Matpower 4.0 - user’smanual, steady-state operations, planning and analysis tools for powersystems research and education,” Power Systems, IEEE Transactions on,no. 1, vol. 26, pp. 12–19, 2011.

[13] P. K. Iyambo and R. Tzoneva, “Transient stability analysis of the ieee14-bus electric power system,” in AFRICON 2007, 2007, pp. 1–9.

355355355